 The cows and the horses will plow the fields The sheep and the goats will cook the leaves The ducks and the foes they break the corn The chickens and the geese keep the nest they swore And up on the barn with watchful eyes The hogs and the pigs will supervise all the animal farm People aren't cruel and they just don't care That everyone works and everyone shares all the animal farm The sheep and the goats will plow the fields The goats and the pigs will supervise all the animal farm The sheep and the goats will supervise all the animal farm The sheep and the goats will supervise all the animal farm This is my father's farm He has goats and sheep He started out only this 18th livestock But because my father is a very good farmer And he knows how to feed the livestock And looks after them These sheep multiply 4 times in a very short time Look we now have 180 livestock This means they have multiplied 10 times in a short period Hey big boy You have forgotten your head again Hi viewers Little Charlie is right You know good grazing and water make our sheep multiply here on the farm What were you saying 10 times 18 was again Charlie? 10 times 18 is 180 That's right And when it get time to divide the sheep I'm sure your father will remember his kin farming a system I want half of them Well that can only happen if the livestock are divided between only two people Anyway you should by now be able to do much more complex multiplication and division problems than that Right viewers It is good to have your company Today in program 1 in our brand new mathematic video series for grade 6 learners We look at basic mathematical operations And specifically multiplication and division with large numbers After watching this lesson You should be able to multiply up to a 4 digit number by a 2 digit number with answers less than or equal to 100,000 And divide a 5 digit number by a 2 digit number Welcome and enjoy the program All our losses in life were so temporarily and harmless Well, let's look at some ways in which we can multiply and divide our things We know that if we buy 3 packets of apples And there are 6 apples in each packet How many apples will you have together? That's so easy ma'am 3 multiplied by 6 There will be 18 apples all together Well done But it gets harder when the numbers get bigger Remember Well, as these boys obviously know quite well Multiplication is repeated addition The symbol we use for multiplication in mathematics is a small cross For example, when we say 7 multiplied by 2 equals 14 We write it as follows 7 times 2 equals 14 It is shorter to say 7 times Rather than 7 multiplied by all the time So we can simply read 7 times 2 is 14 Okay, so let's look at large numbers To multiply a large number with another number We write the numbers vertically Let's take an example 2 times 6 equals 12 With in brackets 6 plus 6 equals 12 In mathematics, it is important to write down the equations As seeing them in writing helps us to understand better Alright, looking at the equation 2 times 6 equals 12 With in brackets 6 plus 6 equals 12 We now have to find a common multiplier To simplify the equation 3 looks like such a multiplier We can now write the equation as follows We know that 2 times 6 is 12 Which can be written also as 4 times 3 In order to get a 3 on the left-hand side of the equation Are you still with me? Okay Let's look the right-hand side We have 6 plus 6 equals 12 in brackets Which we know can also be written as 3 plus 3 plus 3 plus 3 equals 12 As you see on the screen Before we go to a bigger number to multiply Let's talk about some terms used in multiplication Let's say we have a number like 6245 That's really big number, right? Now This number consists of 4 digits There are 4 numbers in this amount So regardless of what the number is in total If it takes up 4 spaces The ones that tens and hundreds And the thousands 4 places in total It is a 4 digit number The next term that we should know in multiplication Is that we call the biggest number of the 2 In the multiplication problem The multiplier factor The smaller number that we are multiplying it with Is known as the multiplicand And the answer is the product A product is the result of the multiplication Of 2 or more numbers So in the multiplication problem Where we are looking for the product of 6245 Multiplied by 15 Then 6245 is the multiplier factor Write the multiplicand factor 15 in a vertical column Underneath it And the product Or the answer we get Is written in vertical columns Underneath the earlier numbers My head hurts Mathematics is so hard Many people think math is hard But many people also love mathematics Because it can be a lot of fun Here is a math joke for you What did one math book say to the other? Ahahaha What did it say? It said Don't bother me I've got my own problems Aha That's a nice one Have you got another one? Yes I do Okay Here If there were a thousand sheep And six of them jump over the fence How many would be left? None, Miss This looks like an interesting discussion May I join you? Yes, you may have a seat Young men You don't know your math Miss, you don't know your seat When one goes, they all go Haha Okay Let's say I had five coconuts And I gave you three How many would I have left? I don't know, Miss We don't have coconuts In our school We do all our maths Only with apples and oranges You boys are too clever Last one If I had seven oranges In one hand And eight oranges in the other What would I have? Very big hand Haha I guess you are right But now Since we are multiplying What if you have got ten dollars From ten different people? What would you have? A new buy Haha You are very clever And you should not be afraid of mathematics There are really just a few rules With regard to multiplication And once you know them You will find math as easy as a spy Let's look at the rule of multiplying With large numbers Firstly Let's say the multiplicand Is a one digit number As in this problem Calculate seven hundred and sixty five times nine With this problem We write a smaller number Nine under the larger number Seven hundred and sixty five And then calculate the multiplication Multiply the single digit number With a bigger number in the first row Starting with a digit in on the right Nine times five is forty five And we write the five underneath the five And nine in the same vertical column Add a small four over With the six to remember it Okay Now nine times six is fifty four Plus that small four Gives fifty eight So we write the eight underneath the six In the second column from the right While the five is written with the seven In the top row of numbers To remember to edit later Okay So nine times seven is sixty three Plus the five gives sixty eight Again we write down the eight first And since there are no more numbers In the first row to multiply nine with The six is simply written on the right hand side of eight The answer is six thousand eight hundred and eighty five Now let's calculate multiplication Of a four digit number by a two digit number I'm sure you are ready for it now Let's multiply the number nine thousand five hundred and thirty eight By the two digit number seventy Again we write the biggest number in the first row With a multiplier seventy Plays vertically in columns Underneath the first two columns from the right Multiplying nine thousand five hundred and thirty eight by seventy Is quicker than multiplying seventy by nine thousand five hundred and thirty eight Because seventy contains a zero Which makes it easier Immediately we can place a zero in the units column on the right Because we know that zero times all of the numbers in the first row Will still yield zero Now we work with the second number in the multiplicand namely seven And again we multiply with the numbers from right to left in the first row So seven times eight is fifty six We place the six in the second digit position And carry over the five to the second digit position The tenths to add later Seven times three is twenty one Plus the five we carried over Gives twenty six We place the six in the third digit position Under the hundreds where it belongs And remember to carry over the two Again to the five in the first row Now we multiply seven by five and get thirty five Plus the two we carried over So the seven goes to the fourth digit position Under the thousands And yes It was thirty seven So the three goes up to the nine To add up later Seven times nine is sixty three Plus three And the sixty six is written in the columns from right to left in the last row We see the answer is six hundred and sixty seven thousand Six hundred and sixty You know what you're thinking You are saying you made it easy for yourself with the seventy You did nothing but put a zero as the first calculation So that's why we will do one last example of multiplying with four digits Using a two digit multiplier which is not zero Have a look We will calculate multiplying eight thousand seven hundred and sixty nine by sixty eight We begin by placing the sixty eight under columns vertically below the bigger number One thousand seven hundred and sixty nine As before we now start with eight times nine Then six Then seven And one Always adding up the numbers we carried over So eight times nine is seventy two With the two going to the far right position under the other ones column And seven being carried over to the tens To add to six later Then eight times six is forty eight Plus seven is fifty five Five in the tens position And five carried to the hundreds on top Eight times seven then is fifty six Plus five is sixty one Six is carried over Eight times one is eight Plus the six carried over is fourteen Which is written as such Now all we have done was to multiply one thousand seven hundred and sixty nine by eight so far Let's continue The next thing we have to do is to multiply the same big number by sixty Yes Not six but sixty The six stands in the tens position Doesn't it? Okay We have already multiplied by the number which occupies the ones So we can place a zero in the far right position This means we really multiply only by sixty now We have dealt with the zero of the sixty Now we continue Six times nine is fifty four With the four being written in the second column with the tens And the five carried over to the six above to add up later Similarly six times six is thirty six Plus the five which gives us forty one We write down one in the third position under the hundreds And four goes up to add later to seven Okay so far Now Six times seven is forty two Write down the two And the four goes added to one in the top row Lastly We say six times one is six Plus the four And we get ten This means that one thousand seven hundred and sixty nine multiplied by sixty is a hundred and six thousand one hundred and forty The rest of the problem is no problem at all We simply add up those two numbers Remember not to confuse the columns So fourteen thousand one hundred and fifty two plus hundred and six thousand one hundred and forty gives a total of one hundred and twenty thousand two hundred and ninety two So man, is division also easy like you have shown us about multiplication? Even easier Charlie If you have six apples and share them equally amongst three How many apples will each person get? Two apples must You are right Charlie But I'm sure you are going to show us how to divide well much larger numbers Just like we have learned at the beginning of the program that multiplication is repeated addition Division is repeated subtraction For example, twelve divided by six is two This means that we can deduct or subtract or take away six from twelve two times Then we will be left with nothing Let's try that again Twelve divided by four is three We can also say that we can subtract four three times from twelve The number that we subtract from the biggest number every time is known as the divisor We can also say that division and does multiplication And involves a number called the dividend being divided by another number called the divisor The biggest number in the other word is the dividend and the number it is divided by is the divisor By the way, have you noticed? The symbol used for division is this one And division and multiplication can be used to test and confirm one another like this We know that nine times eight is seventy two This means that if we divide seventy two by nine, it should give eight And similarly, if we divide seventy two by eight, we should get an answer of nine If forty eight divided by eight is six, then eight times six should be forty eight The second calculation should confirm that the first was correct Let's do a calculation with a single digit divisor and then a double digit divisor We will calculate six hundred ninety two divided by four As division is the inverse of multiplication We start by dividing four into the number in the column farthest to the left, the biggest value Dividing four into six gives us one, which we write at the top Two remains, and we can carry this into the tenth column to make twenty nine Now twenty nine divided by four is seven, with a reminder of one Again, the one is the tenth, which we carry into the unit column to make twelve Finally, twelve divided by four is three, thus six hundred ninety two divided by four is one hundred and seventy three Quite straightforward, isn't it? Now, let's try a double digit number We want to divide twenty five thousand four hundred and eighty nine by sixteen We could do it like this We simplify the number so that four can easily divide into it And then we have twenty four thousand plus one thousand two hundred plus two hundred eighty plus nine divided by sixteen Now divide four into each of these numbers and we get six thousand plus three hundred plus seventy plus two reminder one Now we divide four into these numbers and we get one thousand five hundred plus seventy five plus eighteen reminder one We can also test our answer by multiplying the answer or quotient one thousand five hundred and ninety three remain one Which, of course, we call the dividend by the divisor which is sixteen The calculation of this quickly shows that our answer